Stability of natural convection in a vertical slot

Vest, Charles M.; Arpacı, Vedat S.

doi:10.1017/s0022112069001467

Cited by 193 publications

(74 citation statements)

References 6 publications

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“…For values of Pr < 12.7, the parallel flow undergoes a transition to a stationary multicell flow pattern when the Grashof number exceeds a critical value. This transition has been observed experimentally by Vest and Arpaci [6]. The critical disturbance modes are found to be travelling waves when Pr > 12.…”

Section: Introductionsupporting

confidence: 75%

“…The stability of natural convection of a Newtonian viscous fluid which is confined between two parallel vertical plates maintained at constant and different temperatures provides one of the simplest cases of an interaction between buoyancy and shearing forces and has been investigated analytically, numerically and experimentally [1][2][3][4][5][6][7][8][9]. Instability of the base flow in such a vertical fluid layer occurs when the Grashof number becomes greater than a certain critical value.…”

Section: Introductionmentioning

confidence: 99%

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Stability of natural convection in a vertical couple stress fluid layer

Shankar

Kumar

Shivakumara

2014

International Journal of Heat and Mass Transfer

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a b s t r a c tThe stability of buoyancy-driven parallel shear flow of a couple stress fluid confined between vertical plates is investigated by performing a classical linear stability analysis. The plates are maintained at constant but different temperatures. A modified Orr-Sommerfeld equation is derived and solved numerically using the Galerkin method with wave speed as the eigenvalue. The critical Grashof number G c ; critical wave number a c and critical wave speed c c are computed for wide ranges of couple stress parameter K c and the Prandtl number Pr. Based on these parameters, the stability characteristics of the system are discussed in detail. The value of Prandtl number, at which the transition from stationary to travelling-wave mode takes place, increases with increasing K c . The couple stress parameter shows destabilising effect on the convective flow against stationary mode, while it exhibits a dual behaviour if the instability is via travelling-wave mode. The streamlines and isotherms presented demonstrate the development of complex dynamics at the critical state.

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Section: Introductionsupporting

confidence: 75%

Section: Introductionmentioning

confidence: 99%

Stability of natural convection in a vertical couple stress fluid layer

Shankar

Kumar

Shivakumara

2014

International Journal of Heat and Mass Transfer

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“…The stability aspects of this classical problem for the Newtonian fluid flow are studied extensively [1][2][3][4][5] . One important observation made was that the parallel flow undergoes a transition to a stationary multicell flow pattern for values of Prandtl number, Pr < 12.7 when the Grashof number exceeds a critical value and this theoretically observed fact was confirmed experimentally by Vest and Arpaci [6] . The stability of fluid flows under the influence of electric/magnetic field has also received equal importance in the literature.…”

Section: Introductionmentioning

confidence: 74%

Stability of natural convection in a vertical dielectric couple stress fluid layer in the presence of a horizontal AC electric field

Shankar

Kumar

Shivakumara

2016

Applied Mathematical Modelling

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a b s t r a c tThe combined effect of couple stresses and a uniform horizontal AC electric field on the stability of buoyancy-driven parallel shear flow of a vertical dielectric fluid between vertical surfaces maintained at constant but different temperatures is investigated. Applying linear stability theory, stability equations are derived and solved numerically using the Galerkin method with wave speed as the eigenvalue. The critical Grashof number G c , the critical wave number a c and the critical wave speed c c are computed for wide ranges of couple stress parameter c , AC electric Rayleigh number R ea and the Prandtl number Pr . Based on these parameters, the stability characteristics of the system are discussed in detail. The value of Prandtl number at which the transition from stationary to travelling-wave mode takes place is found to be independent of AC electric Rayleigh number even in the presence of couple stresses but increases significantly with increasing c . Moreover, the effect of increasing R ea is to instill instability, while the couple stress parameter shows destabilizing effect in the stationary mode but it exhibits a dual behavior if the instability is via travelling-wave mode. The streamlines and isotherms presented demonstrate the development of complex dynamics at the critical state.

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“…This result, due to Jones & Furry (1946), and used by Batchelor (1954) and many others (Vest & Arpaci 1969;Hart 1971;Gershuni & Zhukhovitskii 1976;Nagata & Busse 1983;Daniels 1985;Chait & Korpela 1989) in the analysis of tall cavities, describes the flow between infinite parallel plane vertical walls. It satisfies (3.18) at X = ±1/2 but not at Z = ±1/2.…”

Section: The Large-a Limitmentioning

confidence: 92%

Fully developed laminar buoyant flow in vertical cavities and ducts of bounded section

McBain

1999

J. Fluid Mech.

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The fully developed flow in a vertical cavity or duct subject to horizontal heating is considered. Solutions of the Boussinesq equations are obtained for rectangular and elliptic sections, in terms of Fourier series and polynomials, respectively. Both generalize the familiar odd-symmetric cubic profile of the plane cavity. Uniqueness is demonstrated under the restriction that the flow is independent of height. For cavities with rectangular sections, it is predicted and verified that the flow in the plane of spanwise symmetry is practically independent of the span if this exceeds 1.7 times the breadth.

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Stability of natural convection in a vertical slot

Cited by 193 publications

References 6 publications

Stability of natural convection in a vertical couple stress fluid layer

Stability of natural convection in a vertical couple stress fluid layer

Stability of natural convection in a vertical dielectric couple stress fluid layer in the presence of a horizontal AC electric field

Fully developed laminar buoyant flow in vertical cavities and ducts of bounded section

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